Find the equation of the line passing through the point (1, 4) and intersecting the line x - 2y - 11 = 0 on the y-axis.

Since line x - 2y - 11 = 0 intersects y-axis, the point where it will intersect there x-coordinate = 0.

So, putting x = 0 in equation,

⇒ 0 - 2y - 11 = 0
⇒ -2y = 11
⇒ y = -$\dfrac{11}{2}$

Coordinates = $\Big(0, -\dfrac{11}{2}\Big)$

So, the line passes through (1, 4) and $\Big(0, -\dfrac{11}{2}\Big)$.

The equation of the line joining two points is given by,

$y - y$1 = \dfrac{y2 - y1}{x2 - x1}(x - x1)

Putting values we get,

$\Rightarrow y - 4 = \dfrac{-\dfrac{11}{2} - 4}{0 - 1}(x - 1) \\[1em] \Rightarrow y - 4 = \dfrac{\dfrac{-11 - 8}{2}}{-1}(x - 1) \\[1em] \Rightarrow y - 4 = \dfrac{19}{2}(x - 1) \\[1em] \Rightarrow 2(y - 4) = 19(x - 1) \\[1em] \Rightarrow 2y - 8 = 19x - 19 \\[1em] \Rightarrow 19x - 2y - 19 + 8 = 0 \\[1em] \Rightarrow 19x - 2y - 11 = 0.$

Hence, equation of line is 19x - 2y - 11 = 0.